Exact frequency response analysis of axially loaded beams with viscoelastic dampers

A method is proposed for frequency response analysis of Euler-Bernoulli beams acted upon by a constant axial load, and carrying an arbitrary number of translational and rotational dampers with Kelvin-Voigt viscoelastic behavior. The method relies on the theory of generalized functions to handle the discontinuities of the response variables, within a standard 1D formulation of the equation of motion. Starting from the exact dynamic Green's functions of the bare beam, i.e. the beam without dampers, exact closed-form expressions are derived for the frequency response of the beam with dampers, subjected to harmonically varying, arbitrarily placed transverse point/polynomial loads, which hold for any number of dampers. Further, free vibration solutions are obtained from a characteristic equation built as determinant of a 4 x 4 matrix, regardless of the number of dampers. Numerical applications show the advantages of the proposed exact solutions. (C) 2016 Elsevier Ltd. All rights reserved.